The origin and propagation of nonlinear electrostatic waves in dusty plasma have drawn the attention of researchers in the last few decades after the first prediction of the existence of these waves in Saturn's ring by Bliokh and Yarashenko in 1985 [1]}, after which scientists discovered several new modes of nonlinear excitations, e.g., dust ion acoustic waves (DIAWs) [2]}, dust acoustic waves (DAWs) [3]}, dust lattice waves (DLWs) [4]}, etc. Dust ion acoustic solitary structures are a type of dust-ion-acoustic wave (DIAW) are formed in a plasma system due to the compromise between the dispersion and the nonlinearity and [5]} form stable hump or dip shaped structures. In a DIAW, the mass density of ions is considered to provide the inertia, while the electrons thermal pressure is assumed to give the restoring force to generate the wave, and the negatively charged dust species are approximated to remain static. Viking Satellite [6]}and THEMIS mission [7]} have already identified this type of wave in both spaces (viz., solar atmosphere [8]}, Saturn's magnetosphere [8]}, pulsar magnetosphere [10]}, active galactic nuclei [11]}, neutron star's polar region [12]}, etc.) and laboratory environments (viz., semiconductor plasmas [11]}, cathode discharge [10]}, tokamaks [11]}, etc.).
